Machine translation (MT) research is most typically English-centric. In recent years, massively multilingual translation systems have also been increasingly popular. However, efforts purposefully focused on less-resourced languages are less widespread. In this paper, we focus on MT from and into the Estonian language. First, emphasizing the importance of data availability, we generate and publicly release a back-translation corpus of over 2 billion sentence pairs. Second, using these novel data, we create MT models covering 18 translation directions, all either from or into Estonian. We re-use the encoder of the NLLB multilingual model and train modular decoders separately for each language, surpassing the original NLLB quality. Our resulting MT models largely outperform other open-source MT systems, including previous Estonian-focused efforts, and are released as part of this submission.